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 A182025 a(n) = 31*binomial(2*n,n-4) + Sum_{i=1..n-4} binomial(2*n,n-4-i)*(4+i). 1
 0, 0, 0, 0, 31, 315, 2112, 11830, 60060, 287028, 1317840, 5883768, 25741485, 110921525, 472431960, 1993896450, 8354335080, 34799391000, 144259293600, 595644532560, 2451231964350, 10059146122662, 41181227878560, 168246990214380, 686162857445736, 2794089011606200, 11362424624634720, 46152024284293200, 187266363241782825 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Olivia Beckwith, Victor Luo, Stephen J. Miller, Karen Shen, Nicholas Triantafillou, Distribution of Eigenvalues of Weighted, Structured Matrix Ensembles, arXiv preprint arXiv:1112.3719 [math.PR], 2011-2012. Olivia Beckwith, Victor Luo, Stephen J. Miller, Karen Shen, Nicholas Triantafillou, Distribution of Eigenvalues of Weighted, Structured Matrix Ensembles, Electronic Journal of Combinatorial Number Theory, Volume 15 (2015) #A21. FORMULA Conjecture: 558*(n-4)*(n+4)*a(n) +7*(-631*n^2+777*n+4600)*a(n-1) +4370*(n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Aug 08 2012 MAPLE f:=n->31*binomial(2*n, n-4)+add(binomial(2*n, n-4-i)*(4+i), i=1..n-4); [seq(f(n), n=0..40)]; MATHEMATICA Table[31*Binomial[2n, n-4]+Sum[Binomial[2n, n-4-i](4+i), {i, n-4}], {n, 0, 30}] (* Harvey P. Dale, May 24 2016 *) PROG (PARI) a(n) = 31*binomial(2*n, n-4) + sum(i=1, n-4, binomial(2*n, n-4-i)*(4+i)); \\ Michel Marcus, Apr 05 2019 CROSSREFS Cf. A182026. Sequence in context: A221306 A142382 A137318 * A221189 A029813 A138697 Adjacent sequences:  A182022 A182023 A182024 * A182026 A182027 A182028 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 06 2012 STATUS approved

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Last modified August 3 05:55 EDT 2020. Contains 336197 sequences. (Running on oeis4.)